Congratulations both for finding your ancestors, and on finding a free(?) geneology source in Ireland.
Patrick Leech is likely the father or older brother. Hopefully, Patrick was a brother as there are no marriage rcds for Patrick Leech prior to 1827.
I'm not sure whether the IFHF or the Louth County Library use the same data sources, or record the same essential elements of information. I suspect they do. In that case, the parents' forenames may never have been rcd'd. The Louth County Library is a member of the IFHF.
You may have a verrry slim chance of finding marriage rcds for Joseph and Ann's parents; Abt 10 of 24 parishes were keeping at least some marriage rcds B4 1800. You would have to match B rcds using surnames only for each of the 10 parishes. This is doable, but tedious.
Contact the firstname.lastname@example.org for help.